Adaptation under probabilistic error for estimating linear functionals

T. Tony Cai and Mark G. Low

Journal of Multivariate Analysis, 2006, vol. 97, issue 1, 231-245

Abstract: The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic error over a collection of convex parameter spaces. In contrast to mean squared error it is shown that fully rate optimal adaptive estimators can be constructed for probabilistic error. A general construction of such estimators is provided and examples are given to illustrate the general theory.

Keywords: Adaptive; estimation; Confidence; intervals; Gaussian; models; Modulus; of; continuity; Probabilistic; error (search for similar items in EconPapers)
Date: 2006
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